PCA.Biplot {MultBiplotR}

Classical PCA Biplot with added features.

Description

Classical PCA Biplot with added features.

Usage

PCA.Biplot(X, alpha = 1, dimension = 2, Scaling = 5, sup.rows = NULL, 
          sup.cols = NULL, grouping = NULL)

Arguments

X

Data Matrix

alpha

A number between 0 and 1. 0 for GH-Biplot, 1 for JK-Biplot and 0.5 for SQRT-Biplot. Use 2 or any other value not in the interval [0,1] for HJ-Biplot.

dimension

Dimension of the solution

Scaling

Transformation of the original data. See InitialTransform for available transformations.

sup.rows

Supplementary or illustrative rows, if any.

sup.cols

Supplementary or illustrative rows, if any.

grouping

A factor to standardize with the variability within groups

Details

Biplots represent the rows and columns of a data matrix in reduced dimensions. Usually rows represent individuals, objects or samples and columns are variables measured on them. The most classical versions can be thought as visualizations associated to Principal Components Analysis (PCA) or Factor Analysis (FA) obtained from a Singular Value Decomposition or a related method. From another point of view, Classical Biplots could be obtained from regressions and calibrations that are essentially an alternated least squares algorithm equivalent to an EM-algorithm when data are normal.

Value

An object of class ContinuousBiplot with the following components:

Title

A general title

Non_Scaled_Data

Original Data Matrix

Means

Means of the original Variables

Medians

Medians of the original Variables

Deviations

Standard Deviations of the original Variables

Minima

Minima of the original Variables

Maxima

Maxima of the original Variables

P25

25 Percentile of the original Variables

P75

75 Percentile of the original Variables

Gmean

Global mean of the complete matrix

Sup.Rows

Supplementary rows (Non Transformed)

Sup.Cols

Supplementary columns (Non Transformed)

Scaled_Data

Transformed Data

Scaled_Sup.Rows

Supplementary rows (Transformed)

Scaled_Sup.Cols

Supplementary columns (Transformed)

n

Number of Rows

p

Number of Columns

nrowsSup

Number of Supplementary Rows

ncolsSup

Number of Supplementary Columns

dim

Dimension of the Biplot

EigenValues

Eigenvalues

Inertia

Explained variance (Inertia)

CumInertia

Cumulative Explained variance (Inertia)

EV

EigenVectors

Structure

Correlations of the Principal Components and the Variables

RowCoordinates

Coordinates for the rows, including the supplementary

ColCoordinates

Coordinates for the columns, including the supplementary

RowContributions

Contributions for the rows, including the supplementary

ColContributions

Contributions for the columns, including the supplementary

Scale_Factor

Scale factor for the traditional plot with points and arrows. The row coordinates are multiplied and the column coordinates divided by that scale factor. The look of the plot is better without changing the inner product. For the HJ-Biplot the scale factor is 1.

Author(s)

Jose Luis Vicente Villardon

References

Gabriel, K.R.(1971): The biplot graphic display of matrices with applications to principal component analysis. Biometrika, 58, 453-467.

Galindo Villardon, M. (1986). Una alternativa de representacion simultanea: HJ-Biplot. Questiio. 1986, vol. 10, núm. 1.

Gabriel, K. R. AND Zamir, S. (1979). Lower rank approximation of matrices by least squares with any choice of weights. Technometrics, 21(21):489–498, 1979.

Gabriel, K.R.(1998): Generalised Bilinear Regression. Biometrika, 85, 3, 689-700.

Gower y Hand (1996): Biplots. Chapman & Hall.

Vicente-Villardon, J. L., Galindo, M. P. and Blazquez-Zaballos, A. (2006). Logistic Biplots. Multiple Correspondence Analysis and related methods 491-509.

Demey, J., Vicente-Villardon, J. L., Galindo, M. P. and Zambrano, A. (2008). Identifying Molecular Markers Associated With Classification Of Genotypes Using External Logistic Biplots. Bioinformatics 24 2832-2838.

See Also

InitialTransform

Examples

## Simple Biplot with arrows
data(Protein)
bip=PCA.Biplot(Protein[,3:11])
plot(bip)

## Biplot with scales on the variables
plot(bip, mode="s", margin=0.2)

# Structure plot (Correlations)
CorrelationCircle(bip)

# Plot of the Variable Contributions
ColContributionPlot(bip, cex=1)